∫ e17−34x2+17e8x2+32x3−15x4−32x5+48x6−32x7+16x8+e4(34x−34x3+32x4−32x5)+e2x(1−2x2+e8x2+x4+e4(2x−2x3))+ex(8−16x2+8e8x2+8x3−8x5+8x6+e4(16x−16x3+8x4−8x5)) _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 1−2x2+e8x2+x4+e4(2x−2x3) (96x2−128x3−128x4+288x5−192x6+32x7+96x8−64x9+e8(64x4−96x5)+e4(160x3−224x4−96x5+224x6−160x7+96x8)+e2x(2−6x2+2e12x3+6x4−2x6+e8(6x2−6x4)+e4(6x−12x3+6x5))+ex(8−24x3+8e12x3−16x4+32x5+16x6−8x7−8x8+e8(24x2−8x4−16x5−8x6)+e4(24x−8x3−40x4−16x5+24x6+16x7))) ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________1−3x2 +e12 x3 +3x4 −x6 +e8 (3x2 −3x4 )+e4 (3x−6x3 +3x5 ) dx

3.45.58 $\int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 (34 x-34 x^3+32 x^4-32 x^5)+e^{2 x} (1-2 x^2+e^8 x^2+x^4+e^4 (2 x-2 x^3))+e^x (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 (16 x-16 x^3+8 x^4-8 x^5))}{1-2 x^2+e^8 x^2+x^4+e^4 (2 x-2 x^3)}} (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 (64 x^4-96 x^5)+e^4 (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8)+e^{2 x} (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 (6 x^2-6 x^4)+e^4 (6 x-12 x^3+6 x^5))+e^x (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 (24 x^2-8 x^4-16 x^5-8 x^6)+e^4 (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7)))}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 (3 x^2-3 x^4)+e^4 (3 x-6 x^3+3 x^5)} \, dx$

Optimal. Leaf size=31 \[ e^{1+\left (4+e^x-\frac {4 (-1+x) x^2}{e^4+\frac {1}{x}-x}\right )^2} \]

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Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(E^((17 - 34*x^2 + 17*E^8*x^2 + 32*x^3 - 15*x^4 - 32*x^5 + 48*x^6 - 32*x^7 + 16*x^8 + E^4*(34*x - 34*x^3 +

32*x^4 - 32*x^5) + E^(2*x)*(1 - 2*x^2 + E^8*x^2 + x^4 + E^4*(2*x - 2*x^3)) + E^x*(8 - 16*x^2 + 8*E^8*x^2 + 8*

x^3 - 8*x^5 + 8*x^6 + E^4*(16*x - 16*x^3 + 8*x^4 - 8*x^5)))/(1 - 2*x^2 + E^8*x^2 + x^4 + E^4*(2*x - 2*x^3)))*(

96*x^2 - 128*x^3 - 128*x^4 + 288*x^5 - 192*x^6 + 32*x^7 + 96*x^8 - 64*x^9 + E^8*(64*x^4 - 96*x^5) + E^4*(160*x

^3 - 224*x^4 - 96*x^5 + 224*x^6 - 160*x^7 + 96*x^8) + E^(2*x)*(2 - 6*x^2 + 2*E^12*x^3 + 6*x^4 - 2*x^6 + E^8*(6

*x^2 - 6*x^4) + E^4*(6*x - 12*x^3 + 6*x^5)) + E^x*(8 - 24*x^3 + 8*E^12*x^3 - 16*x^4 + 32*x^5 + 16*x^6 - 8*x^7

- 8*x^8 + E^8*(24*x^2 - 8*x^4 - 16*x^5 - 8*x^6) + E^4*(24*x - 8*x^3 - 40*x^4 - 16*x^5 + 24*x^6 + 16*x^7))))/(1

- 3*x^2 + E^12*x^3 + 3*x^4 - x^6 + E^8*(3*x^2 - 3*x^4) + E^4*(3*x - 6*x^3 + 3*x^5)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B] time = 2.10, size = 176, normalized size = 5.68 \begin {gather*} e^{\frac {17 e^8 x^2+8 e^{8+x} x^2+e^{8+2 x} x^2-2 e^{4+2 x} x \left (-1+x^2\right )+e^{2 x} \left (-1+x^2\right )^2-8 e^{4+x} x \left (-2+2 x^2-x^3+x^4\right )+8 e^x (-1+x)^2 \left (1+2 x+x^2+x^3+x^4\right )+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+(-1+x)^2 \left (17+34 x+17 x^2+32 x^3+32 x^4+16 x^6\right )}{\left (1+e^4 x-x^2\right )^2}} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^((17 - 34*x^2 + 17*E^8*x^2 + 32*x^3 - 15*x^4 - 32*x^5 + 48*x^6 - 32*x^7 + 16*x^8 + E^4*(34*x - 34

*x^3 + 32*x^4 - 32*x^5) + E^(2*x)*(1 - 2*x^2 + E^8*x^2 + x^4 + E^4*(2*x - 2*x^3)) + E^x*(8 - 16*x^2 + 8*E^8*x^

2 + 8*x^3 - 8*x^5 + 8*x^6 + E^4*(16*x - 16*x^3 + 8*x^4 - 8*x^5)))/(1 - 2*x^2 + E^8*x^2 + x^4 + E^4*(2*x - 2*x^

3)))*(96*x^2 - 128*x^3 - 128*x^4 + 288*x^5 - 192*x^6 + 32*x^7 + 96*x^8 - 64*x^9 + E^8*(64*x^4 - 96*x^5) + E^4*

(160*x^3 - 224*x^4 - 96*x^5 + 224*x^6 - 160*x^7 + 96*x^8) + E^(2*x)*(2 - 6*x^2 + 2*E^12*x^3 + 6*x^4 - 2*x^6 +

E^8*(6*x^2 - 6*x^4) + E^4*(6*x - 12*x^3 + 6*x^5)) + E^x*(8 - 24*x^3 + 8*E^12*x^3 - 16*x^4 + 32*x^5 + 16*x^6 -

8*x^7 - 8*x^8 + E^8*(24*x^2 - 8*x^4 - 16*x^5 - 8*x^6) + E^4*(24*x - 8*x^3 - 40*x^4 - 16*x^5 + 24*x^6 + 16*x^7)

)))/(1 - 3*x^2 + E^12*x^3 + 3*x^4 - x^6 + E^8*(3*x^2 - 3*x^4) + E^4*(3*x - 6*x^3 + 3*x^5)),x]

[Out]

E^((17*E^8*x^2 + 8*E^(8 + x)*x^2 + E^(8 + 2*x)*x^2 - 2*E^(4 + 2*x)*x*(-1 + x^2) + E^(2*x)*(-1 + x^2)^2 - 8*E^(

4 + x)*x*(-2 + 2*x^2 - x^3 + x^4) + 8*E^x*(-1 + x)^2*(1 + 2*x + x^2 + x^3 + x^4) + E^4*(34*x - 34*x^3 + 32*x^4

- 32*x^5) + (-1 + x)^2*(17 + 34*x + 17*x^2 + 32*x^3 + 32*x^4 + 16*x^6))/(1 + E^4*x - x^2)^2)

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fricas [B] time = 0.88, size = 179, normalized size = 5.77 \begin {gather*} e^{\left (\frac {16 \, x^{8} - 32 \, x^{7} + 48 \, x^{6} - 32 \, x^{5} - 15 \, x^{4} + 32 \, x^{3} + 17 \, x^{2} e^{8} - 34 \, x^{2} - 2 \, {\left (16 \, x^{5} - 16 \, x^{4} + 17 \, x^{3} - 17 \, x\right )} e^{4} + {\left (x^{4} + x^{2} e^{8} - 2 \, x^{2} - 2 \, {\left (x^{3} - x\right )} e^{4} + 1\right )} e^{\left (2 \, x\right )} + 8 \, {\left (x^{6} - x^{5} + x^{3} + x^{2} e^{8} - 2 \, x^{2} - {\left (x^{5} - x^{4} + 2 \, x^{3} - 2 \, x\right )} e^{4} + 1\right )} e^{x} + 17}{x^{4} + x^{2} e^{8} - 2 \, x^{2} - 2 \, {\left (x^{3} - x\right )} e^{4} + 1}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp(4)-2*x^6+6*x^4-6*x^2+2)*exp(x)^2+(8*

x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x^2)*exp(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7

+16*x^6+32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160*x^7+224*x^6-96*x^5-224*x^4+160*x^

3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+288*x^5-128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+

x^4-2*x^2+1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6-8*x^5+8*x^3-16*x^2+8)*exp(x)+17*

x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)*exp(4)+16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp

(4)^2+(-2*x^3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3*x^5-6*x^3+3*x)*exp(4)-x^6+3*x

^4-3*x^2+1),x, algorithm="fricas")

[Out]

e^((16*x^8 - 32*x^7 + 48*x^6 - 32*x^5 - 15*x^4 + 32*x^3 + 17*x^2*e^8 - 34*x^2 - 2*(16*x^5 - 16*x^4 + 17*x^3 -

17*x)*e^4 + (x^4 + x^2*e^8 - 2*x^2 - 2*(x^3 - x)*e^4 + 1)*e^(2*x) + 8*(x^6 - x^5 + x^3 + x^2*e^8 - 2*x^2 - (x^

5 - x^4 + 2*x^3 - 2*x)*e^4 + 1)*e^x + 17)/(x^4 + x^2*e^8 - 2*x^2 - 2*(x^3 - x)*e^4 + 1))

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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp(4)-2*x^6+6*x^4-6*x^2+2)*exp(x)^2+(8*

x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x^2)*exp(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7

+16*x^6+32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160*x^7+224*x^6-96*x^5-224*x^4+160*x^

3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+288*x^5-128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+

x^4-2*x^2+1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6-8*x^5+8*x^3-16*x^2+8)*exp(x)+17*

x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)*exp(4)+16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp

(4)^2+(-2*x^3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3*x^5-6*x^3+3*x)*exp(4)-x^6+3*x

^4-3*x^2+1),x, algorithm="giac")

[Out]

Timed out

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maple [F] time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (2 \,{\mathrm e}^{12} x^{3}+\left (-6 x^{4}+6 x^{2}\right ) {\mathrm e}^{8}+\left (6 x^{5}-12 x^{3}+6 x \right ) {\mathrm e}^{4}-2 x^{6}+6 x^{4}-6 x^{2}+2\right ) {\mathrm e}^{2 x}+\left (8 \,{\mathrm e}^{12} x^{3}+\left (-8 x^{6}-16 x^{5}-8 x^{4}+24 x^{2}\right ) {\mathrm e}^{8}+\left (16 x^{7}+24 x^{6}-16 x^{5}-40 x^{4}-8 x^{3}+24 x \right ) {\mathrm e}^{4}-8 x^{8}-8 x^{7}+16 x^{6}+32 x^{5}-16 x^{4}-24 x^{3}+8\right ) {\mathrm e}^{x}+\left (-96 x^{5}+64 x^{4}\right ) {\mathrm e}^{8}+\left (96 x^{8}-160 x^{7}+224 x^{6}-96 x^{5}-224 x^{4}+160 x^{3}\right ) {\mathrm e}^{4}-64 x^{9}+96 x^{8}+32 x^{7}-192 x^{6}+288 x^{5}-128 x^{4}-128 x^{3}+96 x^{2}\right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{8}+\left (-2 x^{3}+2 x \right ) {\mathrm e}^{4}+x^{4}-2 x^{2}+1\right ) {\mathrm e}^{2 x}+\left (8 x^{2} {\mathrm e}^{8}+\left (-8 x^{5}+8 x^{4}-16 x^{3}+16 x \right ) {\mathrm e}^{4}+8 x^{6}-8 x^{5}+8 x^{3}-16 x^{2}+8\right ) {\mathrm e}^{x}+17 x^{2} {\mathrm e}^{8}+\left (-32 x^{5}+32 x^{4}-34 x^{3}+34 x \right ) {\mathrm e}^{4}+16 x^{8}-32 x^{7}+48 x^{6}-32 x^{5}-15 x^{4}+32 x^{3}-34 x^{2}+17}{x^{2} {\mathrm e}^{8}+\left (-2 x^{3}+2 x \right ) {\mathrm e}^{4}+x^{4}-2 x^{2}+1}}}{{\mathrm e}^{12} x^{3}+\left (-3 x^{4}+3 x^{2}\right ) {\mathrm e}^{8}+\left (3 x^{5}-6 x^{3}+3 x \right ) {\mathrm e}^{4}-x^{6}+3 x^{4}-3 x^{2}+1}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp(4)-2*x^6+6*x^4-6*x^2+2)*exp(x)^2+(8*x^3*ex

p(4)^3+(-8*x^6-16*x^5-8*x^4+24*x^2)*exp(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7+16*x^

6+32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160*x^7+224*x^6-96*x^5-224*x^4+160*x^3)*exp

(4)-64*x^9+96*x^8+32*x^7-192*x^6+288*x^5-128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+x^4-2*

x^2+1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6-8*x^5+8*x^3-16*x^2+8)*exp(x)+17*x^2*ex

p(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)*exp(4)+16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp(4)^2+

(-2*x^3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3*x^5-6*x^3+3*x)*exp(4)-x^6+3*x^4-3*x

^2+1),x)

[Out]

int(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp(4)-2*x^6+6*x^4-6*x^2+2)*exp(x)^2+(8*x^3*ex

p(4)^3+(-8*x^6-16*x^5-8*x^4+24*x^2)*exp(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7+16*x^

6+32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160*x^7+224*x^6-96*x^5-224*x^4+160*x^3)*exp

(4)-64*x^9+96*x^8+32*x^7-192*x^6+288*x^5-128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+x^4-2*

x^2+1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6-8*x^5+8*x^3-16*x^2+8)*exp(x)+17*x^2*ex

p(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)*exp(4)+16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp(4)^2+

(-2*x^3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3*x^5-6*x^3+3*x)*exp(4)-x^6+3*x^4-3*x

^2+1),x)

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maxima [B] time = 16.15, size = 917, normalized size = 29.58 \begin {gather*} e^{\left (16 \, x^{4} + 32 \, x^{3} e^{4} - 32 \, x^{3} + 48 \, x^{2} e^{8} - 64 \, x^{2} e^{4} + 8 \, x^{2} e^{x} + 80 \, x^{2} + 64 \, x e^{12} - 96 \, x e^{8} + 160 \, x e^{4} + 8 \, x e^{\left (x + 4\right )} - 8 \, x e^{x} - 96 \, x + \frac {16 \, x e^{28}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} - \frac {32 \, x e^{24}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} + \frac {112 \, x e^{20}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} + \frac {96 \, x e^{20}}{x^{2} - x e^{4} - 1} - \frac {160 \, x e^{16}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} - \frac {160 \, x e^{16}}{x^{2} - x e^{4} - 1} + \frac {224 \, x e^{12}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} + \frac {416 \, x e^{12}}{x^{2} - x e^{4} - 1} - \frac {192 \, x e^{8}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} - \frac {416 \, x e^{8}}{x^{2} - x e^{4} - 1} + \frac {112 \, x e^{4}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} + \frac {352 \, x e^{4}}{x^{2} - x e^{4} - 1} + \frac {8 \, x e^{\left (x + 12\right )}}{x^{2} - x e^{4} - 1} - \frac {8 \, x e^{\left (x + 8\right )}}{x^{2} - x e^{4} - 1} + \frac {16 \, x e^{\left (x + 4\right )}}{x^{2} - x e^{4} - 1} - \frac {8 \, x e^{x}}{x^{2} - x e^{4} - 1} - \frac {32 \, x}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} - \frac {128 \, x}{x^{2} - x e^{4} - 1} + \frac {16 \, e^{24}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} + \frac {16 \, e^{24}}{x^{2} - x e^{4} - 1} - \frac {32 \, e^{20}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} - \frac {32 \, e^{20}}{x^{2} - x e^{4} - 1} + \frac {96 \, e^{16}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} + \frac {176 \, e^{16}}{x^{2} - x e^{4} - 1} - \frac {128 \, e^{12}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} - \frac {256 \, e^{12}}{x^{2} - x e^{4} - 1} + \frac {144 \, e^{8}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} + \frac {416 \, e^{8}}{x^{2} - x e^{4} - 1} - \frac {96 \, e^{4}}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} - \frac {320 \, e^{4}}{x^{2} - x e^{4} - 1} + \frac {8 \, e^{\left (x + 8\right )}}{x^{2} - x e^{4} - 1} - \frac {8 \, e^{\left (x + 4\right )}}{x^{2} - x e^{4} - 1} + \frac {8 \, e^{x}}{x^{2} - x e^{4} - 1} + \frac {32}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 2\right )} + 2 \, x e^{4} + 1} + \frac {144}{x^{2} - x e^{4} - 1} + 80 \, e^{16} - 128 \, e^{12} + 272 \, e^{8} - 224 \, e^{4} + e^{\left (2 \, x\right )} + 8 \, e^{\left (x + 8\right )} - 8 \, e^{\left (x + 4\right )} + 16 \, e^{x} + 129\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp(4)-2*x^6+6*x^4-6*x^2+2)*exp(x)^2+(8*

x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x^2)*exp(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7

+16*x^6+32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160*x^7+224*x^6-96*x^5-224*x^4+160*x^

3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+288*x^5-128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+

x^4-2*x^2+1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6-8*x^5+8*x^3-16*x^2+8)*exp(x)+17*

x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)*exp(4)+16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp

(4)^2+(-2*x^3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3*x^5-6*x^3+3*x)*exp(4)-x^6+3*x

^4-3*x^2+1),x, algorithm="maxima")

[Out]

e^(16*x^4 + 32*x^3*e^4 - 32*x^3 + 48*x^2*e^8 - 64*x^2*e^4 + 8*x^2*e^x + 80*x^2 + 64*x*e^12 - 96*x*e^8 + 160*x*

e^4 + 8*x*e^(x + 4) - 8*x*e^x - 96*x + 16*x*e^28/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 32*x*e^24/(

x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 112*x*e^20/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) +

96*x*e^20/(x^2 - x*e^4 - 1) - 160*x*e^16/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 160*x*e^16/(x^2 - x

*e^4 - 1) + 224*x*e^12/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 416*x*e^12/(x^2 - x*e^4 - 1) - 192*x*

e^8/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 416*x*e^8/(x^2 - x*e^4 - 1) + 112*x*e^4/(x^4 - 2*x^3*e^4

+ x^2*(e^8 - 2) + 2*x*e^4 + 1) + 352*x*e^4/(x^2 - x*e^4 - 1) + 8*x*e^(x + 12)/(x^2 - x*e^4 - 1) - 8*x*e^(x +

8)/(x^2 - x*e^4 - 1) + 16*x*e^(x + 4)/(x^2 - x*e^4 - 1) - 8*x*e^x/(x^2 - x*e^4 - 1) - 32*x/(x^4 - 2*x^3*e^4 +

x^2*(e^8 - 2) + 2*x*e^4 + 1) - 128*x/(x^2 - x*e^4 - 1) + 16*e^24/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 +

1) + 16*e^24/(x^2 - x*e^4 - 1) - 32*e^20/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 32*e^20/(x^2 - x*e^

4 - 1) + 96*e^16/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 176*e^16/(x^2 - x*e^4 - 1) - 128*e^12/(x^4

- 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 256*e^12/(x^2 - x*e^4 - 1) + 144*e^8/(x^4 - 2*x^3*e^4 + x^2*(e^8

- 2) + 2*x*e^4 + 1) + 416*e^8/(x^2 - x*e^4 - 1) - 96*e^4/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 320

*e^4/(x^2 - x*e^4 - 1) + 8*e^(x + 8)/(x^2 - x*e^4 - 1) - 8*e^(x + 4)/(x^2 - x*e^4 - 1) + 8*e^x/(x^2 - x*e^4 -

1) + 32/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 144/(x^2 - x*e^4 - 1) + 80*e^16 - 128*e^12 + 272*e^8

- 224*e^4 + e^(2*x) + 8*e^(x + 8) - 8*e^(x + 4) + 16*e^x + 129)

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mupad [B] time = 4.82, size = 1097, normalized size = 35.39 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((exp((17*x^2*exp(8) + exp(4)*(34*x - 34*x^3 + 32*x^4 - 32*x^5) + exp(x)*(8*x^2*exp(8) + exp(4)*(16*x - 16*

x^3 + 8*x^4 - 8*x^5) - 16*x^2 + 8*x^3 - 8*x^5 + 8*x^6 + 8) - 34*x^2 + 32*x^3 - 15*x^4 - 32*x^5 + 48*x^6 - 32*x

^7 + 16*x^8 + exp(2*x)*(exp(4)*(2*x - 2*x^3) + x^2*exp(8) - 2*x^2 + x^4 + 1) + 17)/(exp(4)*(2*x - 2*x^3) + x^2

*exp(8) - 2*x^2 + x^4 + 1))*(exp(2*x)*(exp(4)*(6*x - 12*x^3 + 6*x^5) + exp(8)*(6*x^2 - 6*x^4) + 2*x^3*exp(12)

- 6*x^2 + 6*x^4 - 2*x^6 + 2) + exp(4)*(160*x^3 - 224*x^4 - 96*x^5 + 224*x^6 - 160*x^7 + 96*x^8) + exp(x)*(exp(

4)*(24*x - 8*x^3 - 40*x^4 - 16*x^5 + 24*x^6 + 16*x^7) + 8*x^3*exp(12) - 24*x^3 - 16*x^4 + 32*x^5 + 16*x^6 - 8*

x^7 - 8*x^8 - exp(8)*(8*x^4 - 24*x^2 + 16*x^5 + 8*x^6) + 8) + exp(8)*(64*x^4 - 96*x^5) + 96*x^2 - 128*x^3 - 12

8*x^4 + 288*x^5 - 192*x^6 + 32*x^7 + 96*x^8 - 64*x^9))/(exp(4)*(3*x - 6*x^3 + 3*x^5) + exp(8)*(3*x^2 - 3*x^4)

+ x^3*exp(12) - 3*x^2 + 3*x^4 - x^6 + 1),x)

[Out]

exp(17/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((x^4*exp(2*x))/(2*x*exp(4) - 2*x^3*exp(

4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(2*x^2*exp(2*x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^

4 + 1))*exp((2*x*exp(2*x)*exp(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((8*x^4*exp(4

)*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(8*x^5*exp(4)*exp(x))/(2*x*exp(4) -

2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((8*x^2*exp(8)*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(

8) - 2*x^2 + x^4 + 1))*exp(-(16*x^3*exp(4)*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))

*exp(exp(2*x)/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((17*x^2*exp(8))/(2*x*exp(4) - 2*

x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((32*x^4*exp(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^

2 + x^4 + 1))*exp(-(34*x^3*exp(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(32*x^5*ex

p(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(2*x^3*exp(2*x)*exp(4))/(2*x*exp(4) - 2

*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((x^2*exp(2*x)*exp(8))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8)

- 2*x^2 + x^4 + 1))*exp((8*x^3*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(8*x^

5*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((8*x^6*exp(x))/(2*x*exp(4) - 2*x^3*e

xp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(16*x^2*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 +

x^4 + 1))*exp((16*x*exp(4)*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(15*x^4)/(

2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((16*x^8)/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8

) - 2*x^2 + x^4 + 1))*exp((32*x^3)/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(34*x^2)/(

2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(32*x^5)/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(

8) - 2*x^2 + x^4 + 1))*exp(-(32*x^7)/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((48*x^6)/

(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((8*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*ex

p(8) - 2*x^2 + x^4 + 1))*exp((34*x*exp(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))

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sympy [B] time = 11.27, size = 187, normalized size = 6.03 \begin {gather*} e^{\frac {16 x^{8} - 32 x^{7} + 48 x^{6} - 32 x^{5} - 15 x^{4} + 32 x^{3} - 34 x^{2} + 17 x^{2} e^{8} + \left (- 32 x^{5} + 32 x^{4} - 34 x^{3} + 34 x\right ) e^{4} + \left (x^{4} - 2 x^{2} + x^{2} e^{8} + \left (- 2 x^{3} + 2 x\right ) e^{4} + 1\right ) e^{2 x} + \left (8 x^{6} - 8 x^{5} + 8 x^{3} - 16 x^{2} + 8 x^{2} e^{8} + \left (- 8 x^{5} + 8 x^{4} - 16 x^{3} + 16 x\right ) e^{4} + 8\right ) e^{x} + 17}{x^{4} - 2 x^{2} + x^{2} e^{8} + \left (- 2 x^{3} + 2 x\right ) e^{4} + 1}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**3*exp(4)**3+(-6*x**4+6*x**2)*exp(4)**2+(6*x**5-12*x**3+6*x)*exp(4)-2*x**6+6*x**4-6*x**2+2)*ex

p(x)**2+(8*x**3*exp(4)**3+(-8*x**6-16*x**5-8*x**4+24*x**2)*exp(4)**2+(16*x**7+24*x**6-16*x**5-40*x**4-8*x**3+2

4*x)*exp(4)-8*x**8-8*x**7+16*x**6+32*x**5-16*x**4-24*x**3+8)*exp(x)+(-96*x**5+64*x**4)*exp(4)**2+(96*x**8-160*

x**7+224*x**6-96*x**5-224*x**4+160*x**3)*exp(4)-64*x**9+96*x**8+32*x**7-192*x**6+288*x**5-128*x**4-128*x**3+96

*x**2)*exp(((x**2*exp(4)**2+(-2*x**3+2*x)*exp(4)+x**4-2*x**2+1)*exp(x)**2+(8*x**2*exp(4)**2+(-8*x**5+8*x**4-16

*x**3+16*x)*exp(4)+8*x**6-8*x**5+8*x**3-16*x**2+8)*exp(x)+17*x**2*exp(4)**2+(-32*x**5+32*x**4-34*x**3+34*x)*ex

p(4)+16*x**8-32*x**7+48*x**6-32*x**5-15*x**4+32*x**3-34*x**2+17)/(x**2*exp(4)**2+(-2*x**3+2*x)*exp(4)+x**4-2*x

**2+1))/(x**3*exp(4)**3+(-3*x**4+3*x**2)*exp(4)**2+(3*x**5-6*x**3+3*x)*exp(4)-x**6+3*x**4-3*x**2+1),x)

[Out]

exp((16*x**8 - 32*x**7 + 48*x**6 - 32*x**5 - 15*x**4 + 32*x**3 - 34*x**2 + 17*x**2*exp(8) + (-32*x**5 + 32*x**

4 - 34*x**3 + 34*x)*exp(4) + (x**4 - 2*x**2 + x**2*exp(8) + (-2*x**3 + 2*x)*exp(4) + 1)*exp(2*x) + (8*x**6 - 8

*x**5 + 8*x**3 - 16*x**2 + 8*x**2*exp(8) + (-8*x**5 + 8*x**4 - 16*x**3 + 16*x)*exp(4) + 8)*exp(x) + 17)/(x**4

- 2*x**2 + x**2*exp(8) + (-2*x**3 + 2*x)*exp(4) + 1))

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